Knapsack Problems

Guntram Scheithauer
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Guntram Scheithauer: TU Dresden

Chapter Chapter 2 in Introduction to Cutting and Packing Optimization, 2018, pp 19-45 from Springer

Abstract: Abstract The Knapsack Problem is a linear integer programming problem with only one constraint which defines a relation between the variables. In this respect, it is the ‘simplest’ integer optimization problem. Since the knapsack problem already possesses essential difficulties of integer programming, it is subject of numerous investigations. It is well-known that the knapsack problem belongs to the class of NP-hard problems, i.e., with high probability there does not exist any algorithm for the knapsack problem which computes an optimal solution in polynomial time. Within this chapter we present basic techniques to solve the knapsack problem which often can be used in solution approaches for other cutting and packing problems.

Keywords: Knapsack Problem; Integer Optimization Problem; Longest Path Method; Dominance Considerations; Optimal Value Function (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-64403-5_2

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